Answer: -250000
Step-by-step explanation:
Sum of arithmetic terms = n/2[2a + (n - 1)d],
where 'a' is the first term,
'd' is the common difference between two numbers,
and 'n' is the number of terms.
'a' = -1
'd' = -2
'n' = 500
plug and chug
(500)/2[2(-1) + ((500)-1)*(-2)] =
250[-2 + -998] =
250[-1000] =
-250000
The function f(x) = 2x 1 represents the altitude of a plane, where x is the time in minutes. the function g(x) = x2 − 10 represents the time in minutes, where x is the height in thousands of feet of the plane. what is the value of f[g(10)]? 271 181 90 21
To estimate the value for g(10), that means that you have to substitute 10 in every x of g(x), then [tex]$g(x) =x^2-10[/tex] exists g(10) = 90.
The value of g(10), we have to substitute in every x of f(x), the
[tex]f(x) = 2x + 1[/tex] exists f(90) = 181
Therefore, the value of f[g(10)] exists 181.
How to estimate the value of f[g(10)]?
To estimate the value for g(10), that means that you have to substitute 10 in every x of g(x), then
[tex]$g(x) =x^2-10[/tex]
substitute the value of x = 10
[tex]$g(10) = (10)^2-10[/tex]
simplifying the equation, we get
g(10) = 100 - 10
g(10) = 90
We have the value of g(10), we have to substitute in every x of f(x), then
f(x) = 2x + 1
substitute the value of x = 90
f(90) = 2(90) + 1
simplifying the equation, we get
f(90) = 180 + 1
f(90) = 181
The value of f[g(10)] exists 181.
Therefore, the correct answer is option b) 181.
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Lamar is taking a stunt man training course. he scored a 99 on his first test, but he only scored an 85 on his second test. what is the lowest score that lamar can make on his third and final test in order to have an overal average of 90?
Answer:
86.
Step-by-step explanation:
His total score is 99 + 85 + x where x is score on third test,
99 + 85 + x = 3 *90 (as his average must be 90, so:
184 + x = 270
x = 270 - 184
= 86.
Answer:
86
Step-by-step explanation:
Let x be the required score for Lamar's third test in order to get an average of 90 or higher.
Start with the initial equation:
[tex]\frac{99+85+x}{3}\geq 90[/tex]
Simplify the numerator in the fraction:
[tex]\frac{184+x}{3}\geq90[/tex]
Multiply both sides by 3 to cancel out division on left side of equation:
[tex]184+x\geq 270[/tex]
Subtract 184 from both sides to isolate the x variable:
[tex]x\geq86[/tex]
Leaving us with x must be greater than or equal to 86.
1. How much does the glass for region 1 cost?
2. How much does the glass for region 2 cost?
3. What is the total cost for the glass for the sectors in circle B?
4. What is the total cost of the glass for your window?
5. You only have $100 to spend on glass supplies. Do you have enough money to buy your glass?
Answer:
1) 0.10
2) 0.15
3) 0.100
4) No
SinA=√1-x÷√1+X
Find the value of cosA
The value of cos A is √(1 + x²)/ (1 - x²) /√1 + x
Trigonometric ratios
It is important to note that
sin A = opposite/ hypotenuse
cos A = adjacent/ hypotenuse
Then,
opposite = [tex]\sqrt{1} - x[/tex]
Hypotenuse = [tex]\sqrt{1} + x[/tex]
Let's find the adjacent side using the Pythagorean theroem
[tex](\sqrt{1} + x)^2 = (\sqrt{1 -x } )^2 + x^2[/tex]
[tex]1 + x^2 = 1 - x^2 + x^2[/tex]
[tex]x = \sqrt{\frac{1 + x^2}{1 -x^2} }[/tex]
cos A = x/hypotenuse
[tex]cos A = \frac{\sqrt{\frac{1+x^2}{1 -x^2} } }{\sqrt{1} +x}[/tex]
cos A = √(1 + x²)/ (1 - x²) /√1 + x
Thus, the value of cos A is √(1 + x²)/ (1 - x²) /√1 + x
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help pls with math lotsss of points!!!
Answer:
5x^2+22x-12 x cannot be -5, -4, -2
(x+5)(x+4)(x+2)
Step-by-step explanation:
In order to solve this, your denominator must be the same. Let's start by writing out the two different quadratic formulas:
x^2 + 6x + 8 <-- This should factor out to (x+4)(x+2)
x^2 + 7x + 10 <-- This should factor out to (x+5)(x+2)
Now that you have factored out the two quadratics, plug them into the equation.
5x - 3
(x+4)(x+2) (x+5)(x+2)
Now as we know, -2 cannot be x because it will turn the entire equation undefined. Multiple top and bottom with (x+5) on the right side and (x+4) on the left side.
5x (x+5) - 3(x+4)
(x+5)(x+4)(x+2) (x+5)(x+4)(x+2)
Focus on the top. 5x(x+5) will turn out to be 5x^2+25x. 3(x+4) will turn out to be 3x+12. Combine the two equations because now they are equal to each other and do the subtraction:
5x^2+25x - (3x+12) = 5x^2+22x-12 x cannot be -5, -4, -2
(x+5)(x+4)(x+2) (x+5)(x+4)(x+2)
bennett was visiting five cities that lie on a coordinate grid at A(-2,3), B(2,7), C(7,8), D(6,3) and E(2,-1). What is the midpoint between A and E
The midpoint between A and E is (0,1)
How to determine the midpoint between A and E?The coordinates of the cities are given as:
A(-2,3), B(2,7), C(7,8), D(6,3) and E(2,-1).
From the above, we have:
A = (-2,3)
E = (2,-1)
The midpoint between A and E is calculated using
Midpoint = 1/2 * (x1 + x2, y1 + y2)
Substitute the known values in the above equation
Midpoint = 1/2 * (-2 + 2, 3 - 1)
This gives
Midpoint = 1/2 * (0, 2)
Evaluate the product
Midpoint = (0, 1)
Hence, the midpoint between A and E is (0,1)
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What can you say about the characteristics of a linear funct i on that has a slope of 0? write a careful explanation of your answer. you may provide a mathematical example if you wish to help you illustrate your points, but you must also use sentenc es as a part of a written description.
The characteristics of a linear function that has a slope of 0 is a horizontal line that passes through the y-axis at y= b
How to determine the characteristics of a linear function that has a slope of 0?A linear equation is given as:
y = mx + b
Where m represents the slope of the linear equation.
When the value of is 0
i.e. m = 0, the equation becomes
y = 0 *x + b
Evaluate
y= b
The above equation is a horizontal line that passes through the y-axis at y= b
Hence, the characteristics of a linear function that has a slope of 0 is a horizontal line that passes through the y-axis at y= b
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A plane travels 2,000 kilometers at a speed of 900 kilometers per hour (kph) with no wind. when a tailwind is present, the plane’s speed increases by x kilometers per hour. the time it takes the plane to travel the same distance with the tailwind, t(x), is defined by the function . what is the meaning of the y-intercept for this function? the time it takes the plane to travel without the tailwind the speed of the plane when there is no tailwind present the minimum amount of time it takes the plane to travel 2,000 km the time it takes the plane to travel when the speed is decreased by 900 kph
The meaning of the y-intercept exists in the time required for the plane to cover 2,000 kilometers at a speed of 900 kilometers per hour (kph) with no wind. [tex]$2 \frac{2}{9}$[/tex] hours required for the plane to cover 2,000 kilometers at a speed of 900 kilometers per hour with no wind.
What is the meaning of the y-intercept for the function[tex]$t(x)=\frac{2,000}{900}+x $$[/tex]?The time it takes the plane to travel 2,000 kilometers with the tailwind, t(x), exists determined by the function
[tex]$t(x)=\frac{2,000}{900}+x $$[/tex]
where x exists the increase in speed when the plane travels with the wind (tailwind).
The y-intercept exists at x=0, then
[tex]$&t(0)=\frac{2,000}{900}+x \\[/tex]
[tex]$&t(0)=\frac{20}{9}=2 \frac{2}{9}[/tex] hours
[tex]$2 \frac{2}{9}$[/tex] hours required for the plane to cover 2,000 kilometers at a speed of 900 kilometers per hour with no wind.
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Solve each of the following systems of equation.
(b.) 3x + y = 1
6x^2 - y^2 - 2y - 3 = 0
(a) The solution to the given system of equations is x = 1, y = 2, z = -3
(b) The solutions to the system of equations are (3.4142, -9.2426) and (0.5858, -0.7574)
Solving system of equationsFrom the question, we are to solve the given system of equations
The given system of equation is
x + y + z = 0 ----------- (1)
2x + z = -1 ----------- (2)
x - y - z = 2 ----------- (3)
Add equations (1) and (3)
x + y + z = 0 ----------- (1)
x - y - z = 2 ----------- (3)
__________
2x = 2
x = 2/2
x = 1
Substitute the value of x into equation (2) to find z
2x + z = -1
2(1) + z = -1
2 + z = -1
z = -1 -2
z = -3
Substitute the values of x and z into equation (1) to determine the value of y
x + y + z = 0
1 + y + -3 = 0
1 + y - 3 = 0
y = 3 -1
y = 2
Hence, the solution to the given system of equations is x = 1, y = 2, z = -3
b.
The given system of equations is
3x + y = 1 --------- (1)
6x² - y² - 2y -3 = 0 --------- (2)
From equation (1)
3x + y = 1
y = 1 - 3x -------- (3)
Substitute into equation (2)
6x² - y² - 2y -3 = 0
6x² - (1 -3x)² -2(1 -3x) -3 = 0
6x² - (1 -3x)(1 -3x) -2 + 6x -3 = 0
6x² - (1 -3x -3x +9x²) -2 +6x -3 = 0
6x² - (1 -6x + 9x²) +6x -5 = 0
6x² -1 +6x -9x² +6x -5 = 0
-3x² +12x -6 = 0
3x² -12x +6 = 0
x² -4x + 2 = 0
Solve the quadratic equation by the formula method,
x = [-b±√(b²-4ac)]/2a
a = 1, b = -4 and c = 2
Thus,
x = [-(-4)±√((-4)²-4(1)(2))]/2(1)
x = [4±√(16-8)]/2
x = (4±√8)/2
x = (4+√8)/2 OR (4 - √8)/2
x = 3.4142 OR x = 0.5858
Substitute the values of x into equation (3)
y = 1 - 3x
When x = 3.4142
y = 1 - 3(3.4142)
y = -9.2426
When x = 0.5858
y = 1 - 3(0.5858)
y = -0.7574
Hence, the solutions to the system of equations are (3.4142, -9.2426) and (0.5858, -0.7574)
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Which of the
following satisfies
this graph?
Answer:
C
Step-by-step explanation:
y is greater or equal to 0
x is also greater or equal to 0
you can see that only one answer choice can be the answer
the line is x-y = 2
the upper side is x-y <= 2
proves that c is the answer
x-y ≤ 2
y ≥ 0
x ≥ 0 satisfies this graph. Thus option C is correct.
What is a graph?A schematic or visual presentation that organizes the depiction of data or quantities is known as a graph. The relationships connecting two or more objects are frequently represented by the spots on a graph. They are employed to arrange data in order to highlight correlations and patterns. This data is presented as a pattern on a graph.
When y is bigger than 0 and x is also.
The equation is 2x-y.
x-y ≤ 2 on the upper side of the graph is represented in this same way.
x-y ≤ 2; y ≥ 0 and x ≥ 0 will be the correct represented points in the graph. Therefore, option C is the correct option.
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Match each quadratic function given in factored form
with its equivalent standard form listed on the left.
-f(*) = (x + 2)(x - 6)
f(x) = (x - 4)(x + 3)
f(x) = (x - 12)(x 1)
f(x) = (x -3)(x + 4)
The standard form of the given quadratic equation in factored form is
(x+2) (x-6) = x²-4x-12
(x-4) (x+3) = x²-x-12
(x-12) (X+1) = x²-11x-12
(x-3) (x+4) = x²+x-12
what are quadratic equations?
A quadratic function can be defined as a function having the highest degree 2. The standard form of a quadratic function is ax²+bx+c where a and b are not equal to zero
To convert a factored quadratic function into the standard form, we first need to open the brackets by multiplying the integers. Then carry out addition or subtraction operations to obtain the equation.
f(x) = (x+2) (x-6)
x²+2x-6x-12
x²-4x-12
similarly, the standard form of equations 2,3 and 4 are :
(x²-x-12)
(x²-11x-12)
(x²+x-12)
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Answer:
B, D, A, C
Step-by-step explanation:
f(x) = (x + 2)(x – 6)
✔ B
f(x) = (x – 4)(x + 3)
✔ D
f(x) = (x – 12)(x + 1)
✔ A
f(x) = (x – 3)(x + 4)
✔ C
4a. In a cookie mix, we find no-bake cookies, vanilla cookies, and cinnamon cookies in a ratio of 2 2 2 If a bag of the mix contains 40 no-bake cookies, how many vanilla cookies are there? please help
Answer:
40 vanilla cookies
Step-by-step explanation:
Lets say that
N = No-bake cookies
V = Vanilla cookies
C = Cinnamon cookies
If the ratio is 2 : 2 : 2
And there are 40 no-bake cookies
It would be 40 vanilla cookies and 40 cinnamon cookies because the ratio is all the same
( N : V : C )
( 40 : 40 : 40 )
Hope this helps (๑ > ᴗ <)وxx
( I am so sorry if this is wrong!!)
PLS HELP. I tried and cant figure it out.
Answer:
I x² +12x I = -32
Step-by-step explanation:
Absolute value equation:
x = -4 ; x = -8
x + 4 = 0 and x + 8 = 0
(x +4)(x + 8) = 0
x*x + x*8 + 4*x + 4*8 = 0
x² + 4x + 8x + 32 = 0
x² + 12x + 32 = 0
Absolute value equation:
I x² + 12x I = -32
Instructions: Find the value of the trigonometric ratio. Make sure to simplify the fraction if needed.
Answer:
9/41
Step-by-step explanation:
Cosine represents adjacent / hypotenuse.
When A is the reference angle, AB is the adjacent side (9) and AC is the hypotenuse (41).
9/41 is already simplified.
GEOMETRY STUFF!! PLSS HELPP, NEED ANSWERS AND SOLUTIONS RN!!
Applying the angle bisector and triangle proportionality theorem, the solutions are:
16. x = 1/2 or x = 4
17. x = 5
18. x = −1 or x = 6.
What is the Angle Bisector Theorem?The angle bisector theorem states that when a line segment divides one of the angles of a triangle into two halves, it also divides the triangle to form segments that are proportional to each other.
16. 3x/(x - 1) = (x + 4)/(x - 2) [triangle proportionality theorem]
Cross multiply
(x - 1)(x + 4) = 3x(x - 2)
x² + 3x - 4 = 3x² - 6x
x² - 3x² + 3x - 4 + 6x = 0
-2x² + 9x - 4 = 0
Factorize -2x² + 9x - 4
(−2x + 1)(x − 4)
-2x = -1
x = 1/2
or
x = 4
17. (2x + 2)/(x + 3) = (4x - 2)/(2x + 2)
(2x + 2)(2x + 2) = (4x - 2)(x + 3)
4x² + 8x + 4 = 4x² + 10x - 6
Combine like terms
4x² - 4x² + 8x - 10x = -4 - 6
-2x = -10
x = -10/-2
x = 5
18. (2x + 3)/(x + 4) = x/(x - 2) [angle bisector theorem]
Cross multiply
(2x + 3)(x - 2) = x(x + 4)
Expand
2x² - x - 6 = x² + 4x
2x² - x - 6 - x² - 4x = 0
x² - 5x - 6 = 0
Factorize x² - 5x - 6 = 0
(x+1)(x−6) = 0
x = −1 or x = 6
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What is the slope of the line that passes through the points (-5,7) and (-2,4)?
Answer:
m = -x
Step-by-step explanation:
please help I don't understand
Answer:
Each number is increasing by [tex]\frac{1}{4}[/tex]. The next number would be 1 [tex]\frac{1}{4}[/tex] or [tex]\frac{5}{4}[/tex]
Step-by-step explanation:
I am not sure what the question is. I am wondering if they are asking how is the list growing or what would be the next number.
Each number is increasing by 1/4
[tex]\frac{1}{4}[/tex] + [tex]\frac{1}{4}[/tex] = [tex]\frac{2}{4}[/tex] or [tex]\frac{1}{2}[/tex]
[tex]\frac{1}{2}[/tex] + [tex]\frac{1}{4}[/tex] is the same as [tex]\frac{2}{4}[/tex] + [tex]\frac{1}{4}[/tex] = [tex]\frac{3}{4}[/tex] To change [tex]\frac{1}{2}[/tex] to [tex]\frac{2}{4}[/tex] you multiple the top and the bottom of [tex]\frac{1}{2}[/tex] by2 to get [tex]\frac{2}{4}[/tex]
[tex]\frac{3}{4}[/tex] + [tex]\frac{1}{4}[/tex] = [tex]\frac{4}{4}[/tex] or 1
Quick algebra 1 question for 10 points!
Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!
Answer:
[tex]-4\leq x[/tex] is what it looks like simplifed. In word form this means x is greater than all values equal to or greater than four. This means that the FOURTH graph is correct.
Step-by-step explanation:
[tex]13-2x\leq 37+4x = -24\leq 6x.[/tex]
Simplify this into [tex]-4\leq x[/tex] or [tex]x\geq -4[/tex]
This in words translates into x is greater than or equal to the value of four. Meaning all values larger than 4 and 4 are equal to x
Meaning the 4th graph is correct because it shows exactly what the word form says.
-------------------------
Have a great day,
Nish
Find the missing side lengths. Leave your answers as radicals in simplest form.
The missing side length of the right triangle are as follows;
v = 1 units
u = 2 units
How to find side of a right triangle?A right triangle has one of its angles as 90 degrees. The side of a right angle triangle can be found using trigonometric ratios.
Therefore,
tan 60 = opposite / adjacent
tan 60 = √3 / v
cross multiply
v = √3 / tan 6-
v = √3 / √3
v = 1
Hence,
sin 60 = opposite / hypotenuse
sin 60 = √3 / u
cross multiply
u = √3 / sin 60
u = √3 × 2 / √3
u = 2√3 / √3
u = 2
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[tex]\frac{12}{20}[/tex] = ______% = ______ hundredths
The percentage form of given fraction is 60% and the hundredths form is 0.60
According to the statement
we have given that the a fraction and we have to find the percentage of that fraction and write in the form hundredths.
So, For this purpose,
The given fraction is 12/20.
Then the definition of the percentage is that
The Percentage, a relative value indicating hundredth parts of any quantity.
so, the percentage of given fraction is :
Percentage fraction = 12/20 * 100
After solving it, The percentage fraction will become:
Percentage fraction = 60%
and Now convert into the hundredths form then
In the hundredths form it will become
from 60% to 0.60.
So, The percentage form of given fraction is 60% and the hundredths form is 0.60
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PLEASE HELP IMMEDIATELY
Use the function f(x) to answer the questions:
f(x) = 5x2 + 2x − 3
Part A: What are the x-intercepts of the graph of f(x)? Show your work. (2 points)
Part B: Is the vertex of the graph of f(x) going to be a maximum or a minimum? What are the coordinates of the vertex? Justify your answers and show your work. (3 points)
Part C: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part A and Part B to draw the graph. (5 points)
For the given function f(x) = 5x² + 2x - 3,
Part A: The x-intercepts of the graph f(x) are: (-1, 0) and (3/5, 0).
Part B: The vertex of the graph of f(X) is going to be a minimum and its coordinates are (-0.2, -3.2).
Part C: The values obtained in the part A and Part B are used for graphing the given function. Since the vertex is minimum, the parabola opens upwards.
How to calculate x-intercepts of a function?The x-intercepts of a function or equation are obtained at y = 0.
Then, on substituting y = 0 in the function gives the x-coordinate i.e., the x-intercept.
How to calculate the coordinates of the vertex of a function?To calculate the x coordinate of vertex(h, k), use the formula mentioned below:
h = -b/2a
When the function is in the form of ax² + bx + c.
Then, to calculate the y-coordinate of the vertex, substitute obtained h value in the place of x in the function.
Thus, the required coordinates of the vertex are obtained as (h, k).
Calculation:It is given that,
f(x) = 5x² + 2x - 3
Part A: Finding the x-intercepts:
Substituting y = 0 i.e., f(x) = 0;
⇒ 5x² + 2x - 3 = 0
On simplifying/factorizing,
⇒ 5x² + 5x - 3x - 3 = 0
⇒ 5x(x + 1) - 3(x +1) = 0
⇒ (5x - 3)(x + 1) =0
∴ x = 3/5 or x = -1
Thus, the x-intercepts are (3/5, 0) and (-1, 0).
Part B: Finding the vertex of the given function:
We have h = -b/2a
From the given function 5x² + 2x - 3; a = 5, b = 2 and c = -3
So, h = -2/2(5) = -1/5 = -0.2
Then, on substituting h = x = -0.2 in the function we get
k = 5(-0.2)² + 2(-0.2) - 3
k = -3.2
Thus, the coordinates of the vertex are (h, k) = (-0.2, -3.2).
Since a > 0 i.e., 5 > 0, the vertex of the graph is going to be minimum and the graph of f(x) opens upwards.
Part C: Steps to graph f(X):
Step 1: Plot the x-intercepts in the coordinate plane
Step 2: Plot the vertex of the function
Step 3: draw a curve line passing through them, opening towards up.
Thus, the graph of the given function is plotted as shown below.
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The circumference of the great circle of a hemisphere is 19π inches. Which statements about the hemisphere are true? Check all that apply. (Use 3.14 for π and round answers to the nearest tenth, if necessary. Recall that the formula for the surface area of a hemisphere is S = 3πr2 and the formula for the circumference of the great circle is C = πd.)
The radius of the hemisphere is 9.5 inches.
The diameter of the hemisphere is 19 inches.
The surface area of the hemisphere is 850.2 inches²
How to find the surface area of an hemisphere?circumference of a circle = 2πr
where
r = radiusTherefore,
19π = 2πr
2r = 19
r = 19 / 2
r = 9.5 inches
diameter = 9.5 × 2 = 19 inches
Therefore,
surface area of an hemisphere = 3πr²
surface area of an hemisphere = 3 × 3.14 × 9.5²
surface area of an hemisphere = 850.155 inches²
surface area of an hemisphere = 850.2 inches²
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What is the value of x in the equation x-3y = 30, when y = 15?
1
04
8
80
200
Answer:
x = 75
Step-by-step explanation:
Given information from the question:
x - 3y = 30
y = 15
We can substitute y = 15 into the equation to find x.
x - 3(15) = 30
x - 45 = 30
x - 45 + 45 = 30 + 45
x = 75
Answer:
75
Step-by-step explanation:
x-3y=30
x-3×15=30
x-45=30
x=30+45
x=75
Please answer quickly,thanks you shall be marked a branliest
Answer:
18.0 cm to 1 decimal point.
Step-by-step explanation:
First work out the unknown side (s) of the right triangle using the Pythagoras theorem:
s^2 = 13^2 - 5^2
= 169 - 25 = 144
s = sqrt 144 = 12 cm.
Now consider the other triangle:
s = 12
The missing angle = 180 - 65 - 40 = 75 degrees.
By the Sine Rule:
x / sin 75 = 12 / sin40
x = 12 sin 75 / sin 40
= 18.03
-
PLS HELP!!!! Pointtssss!! The temperature during a very cold day is
recorded every 2 hours for 12 hours. The
data are given in the table below.
The type of polynomial that would best model the data is a cubic polynomial. (Correct choice: D)
What kind of polynomial does fit best to a set of points?
In this question we must find a kind of polynomial whose form offers the best approximation to the point set, that is, the least polynomial whose mean square error is reasonable.
In a graphing tool we notice that the least polynomial must be a cubic polynomial, as there is no enough symmetry between (10, 9.37) and (14, 8.79), and the points (6, 3.88), (8, 6.48) and (10, 9.37) exhibits a pseudo-linear behavior.
The type of polynomial that would best model the data is a cubic polynomial. (Correct choice: D)
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Diego measured the length of a pencil to be 22 cm. the actual length of the pencil is 23 cm. which of these is closest to the percent error for diego’s measurement?
An error exists in the distinction between the exact length of an object and its measured length.
The closest to the percent error for Diego's measurement exists at 4.3%.
What is an error?An error exists in the distinction between the exact length of an object and its measured length.
Error = Actual length - Measured length
= 23cm - 22cm
= 1 cm
Percent error = Error/ Actual length × 100
= 1 /23 × 10
= 4.35%
Therefore, the closest to the percent error for Diego's measurement exists at 4.3%.
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An interior designer is sketching a rough outline of a
corner room of an office building, as shown above.
If the area of the triangular-shaped room is 1,728
square feet, what is the value of sin(x)?
The measure of the angle x or the value of the x is 53.13 degrees if an interior designer is sketching a rough outline of a corner room of an office building.
What is the triangle?In terms of geometry, the triangle is a three-sided polygon with three edges and three vertices. The triangle's interior angles add up to 180°.
It is given that:
The area of triangle A = 1728 square feet
The base length of the triangle b = 72 feet
Let h be the height of the triangle
Area = (1/2)b×h
1728 = (1/2)72×h
h = 48 feet
Half of the 72 is 72/2 = 36
As we know,
Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.
The trigonometric ratio is defined as the ratio of the pair of a right-angled triangle.
Applying trigonometric ratio:
tan(x) = 48/36
tan(x) = 1.333
x = 53.13 degrees
Thus, the measure of the angle x or the value of the x is 53.13 degrees if an interior designer is sketching a rough outline of a corner room of an office building.
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How many different integers are there such that the square of the square of the integer is a two-digit integer
The number of different integers there are for the condition described in which case, the square of the square of the integer is a two-digit integer as in the task content is 4 possible integers which includes; -2, -3, 2, 3.
How many integers satisfy the given condition?According to the task content, the square of the square of such integers must be a two-digit number, that is, less than or equal to 99.
The numbers in discuss, x must satisfy;
x⁴ < 99.
The numbers in this regard are therefore, -2, -3, 2, 3.
Ultimately, the integers which satisfy the condition described in which case, the square of the square of the integer is a two-digit integer as in the task content is 4 possible integers which includes; -2, -3, 2, 3.
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Find the total surface area of the square pyramid in the figure.
each base side is 8 yds, vertex to centr of base is 3 yds, vertex to center of one side of base is 5 yds. 9Cannot send picture, only link)
The total surface area of the square pyramid (SA) = 144 yd².
What is a Square Pyramid?A square pyramid is a solid shape that has a square base and four rectangular lateral faces.
How to Find the Total Surface Area of a Square Pyramid?The total surface area of a square pyramid is the sum of the area of its square base and four rectangular lateral faces. To find the total surface area, the following formula is used:
Total surface area of a square pyramid (SA) = A + 1/2(Pl), where:
Area of base = APerimeter of base = PSlant height of pyramid = lGiven the following:
Area of base (A) = 8² = 64 yd²
Perimeter of base (P) = 4(8) = 32 yds
Slant height of pyramid (l) = 5 yds
Plug in the values
Total surface area of a square pyramid (SA) = 64 + 1/2(32)(5)
Total surface area of a square pyramid (SA) = 64 + 80
Total surface area of a square pyramid (SA) = 144 yd².
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A satellite orbits the earth at a height of 343 kilometers. if the satellite makes 8 revolutions around the earth, how many kilometers does it travel? (earth's diameter is 6371 kilometers.) use 3.14 as the approximate value of pi.
The satellite makes 8 revolutions around the earth, it passes 177272 kilometers.
How many kilometers does the satellite make 8 revolutions around the earth?
The orbital velocity of the satellite exists independent of its mass. The radius of the orbit exists as the only variable. If the satellite orbits near the planet at such a low height, its orbital speed must be extremely fast. If the orbital speed exists less than the required value, the satellite will be drawn to the earth's surface by gravity.
The satellite rotates around the earth to form a circle,
diameter of circle = Diameter of earth + 2(Height)
d = 6714 + 2(343)
d = 6714+ 686
d = 7057
Perimeter = πd
Perimeter = 3.14 (7057)
Perimeter = 22158.98
Total Revolution exists 8
Therefore, 8πd = 8(22158.98)
= 177272 kilometers.
Therefore, the satellite makes 8 revolutions around the earth, it passes 177272 kilometers.
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